As a typical method for producing a high-performance piezoelectric film as represented by a large piezoelectricity (usually developing also pyroelectricity as is well known), there is known a type of method, comprising: polarizing a crystalline polymer sheet of, e.g., a polyvinylidene fluoride resin by corona discharge from a pair of electrodes, at least one of which comprises a needle electrode, disposed opposite to each other so as to place the crystalline polymer sheet therebetween, while stretching the crystalline polymer sheet (Patent documents 1 and 2). Incidentally, the terms “sheet” and “film” are used herein so that the former refers to a state before stretching and the latter refers to a state after stretching, regardless of a conventional use thereof in the art that they are differentiated from each other with reference to 250 μm as a boundary thickness. In the above-mentioned methods of Patent documents 1 and 2, needle electrodes are principally used as both of the par of electrodes disposed opposite to each other between which the crystalline polymer sheet is placed, whereas there is also shown a n example wherein a roller electrode is used as one of them (Example 2 of Patent document 2). However, the polymer piezoelectric films thus obtained through the above-mentioned methods still involve irregularities in thickness and piezoelectric performance in a planar direction, and the production conditions thereof have not been satisfactorily stabilized, so that as a present state, it is impossible to obtain a polymer piezoelectric film having a stably large piezoelectricity over a wide area.                Patent document 1: JP-A 55-157801        Patent document 2: EP-A 018802        